Instead of computing partial memberships for each elemental distribution, a membership value for each data point is drawn from a Bernoulli distribution ( that is, it will be assigned to either the first or the second Gaussian ).
22.
While the related beta distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed as a probability, the beta prime distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed in odds.
23.
While the related beta distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed as a probability, the beta prime distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed in odds.
24.
When \ nu = 1, the COM-Poisson distribution becomes the standard Poisson distribution and as \ nu \ to \ infty, the distribution approaches a Bernoulli distribution with parameter \ lambda / ( 1 + \ lambda ).
25.
The kurtosis goes to infinity for high and low values of p, but for p = 1 / 2 the two-point distributions including the Bernoulli distribution have a lower excess kurtosis than any other probability distribution, namely " 2.
26.
Approximating each Bernoulli distribution with a normal distribution with variance " np " ( 1-" p " ), we find that the variance for the fair coin is . 25 " n " and the variance for the biased coin is slightly less.
27.
Where s ^ 2 \, is the ( weighted ) sample variance derived from the observed proportions of success in sets in " Lexis trials " and \ sigma _ 0 ^ 2 is the variance computed from the expected Bernoulli distribution on the basis of the overall average proportion of success.
28.
In probability theory and statistics, the "'Bernoulli distribution "', named after Swiss scientist Jacob Bernoulli, is the probability distribution of a random variable which takes the value 1 with success probability of p and the value 0 with failure probability of q = 1-p.
29.
Therefore, " p " " 1 ( 1 " " p " ) " 1 divided by the Beta function approaches a 2-point Bernoulli distribution with equal probability 1 / 2 at each Dirac delta function end, at 0 and 1, and nothing in between, as ?, ? ?! 0.
30.
For example, the case above of predicted number of beach attendees would typically be modeled with a Poisson distribution and a log link, while the case of predicted probability of beach attendance would typically be modeled with a Bernoulli distribution ( or binomial distribution, depending on exactly how the problem is phrased ) and a log-odds ( or " logit " ) link function.
